Direction Of Group Velocity Research Articles

Low-frequency bandgap and vibration suppression mechanism of a novel square hierarchical honeycomb metamaterial

AbstractThe suppression of low-frequency vibration and noise has always been an important issue in a wide range of engineering applications. To address this concern, a novel square hierarchical honeycomb metamaterial capable of reducing low-frequency noise has been developed. By combining Bloch’s theorem with the finite element method, the band structure is calculated. Numerical results indicate that this metamaterial can produce multiple low-frequency bandgaps within 500 Hz, with a bandgap ratio exceeding 50%. The first bandgap spans from 169.57 Hz to 216.42 Hz. To reveal the formation mechanism of the bandgap, a vibrational mode analysis is performed. Numerical analysis demonstrates that the bandgap is attributed to the suppression of elastic wave propagation by the vibrations of the structure’s two protruding corners and overall expansion vibrations. Additionally, detailed parametric analyses are conducted to investigate the effect of θ, i.e., the angle between the protruding corner of the structure and the horizontal direction, on the band structures and the total effective bandgap width. It is found that reducing θ is conducive to obtaining lower frequency bandgaps. The propagation characteristics of elastic waves in the structure are explored by the group velocity, phase velocity, and wave propagation direction. Finally, the transmission characteristics of a finite periodic structure are investigated experimentally. The results indicate significant acceleration amplitude attenuation within the bandgap range, confirming the structure’s excellent low-frequency vibration suppression capability.

Unidirectional propagation of zero-momentum magnons

We report on experimental observation of unidirectional propagation of zero-momentum magnons in synthetic antiferromagnet consisting of strained CoFeB/Ru/CoFeB trilayer. Inherent non-reciprocity of spin waves in synthetic antiferromagnets with uniaxial anisotropy results in smooth and monotonous dispersion relation around Gamma point, where the direction of the phase velocity is reversed, while the group velocity direction is conserved. The experimental observation of this phenomenon by intensity-, phase-, and time-resolved Brillouin light scattering microscopy is corroborated by analytical models and micromagnetic simulations.

Propagation of elastic waves in fibrous composite with general anisotropy from two families of obliquely inclined fibers

AbstractAn isotropic elastic solid reinforced with two families of aligned fibres behaves anisotropic to any deformation. For arbitrary orientation of fibres in either family, one set of fibres may be inclined obliquely to the aligned fibres in other family. A plane that contains the two families of aligned fibres becomes the plane of symmetry for composite material to exhibit monoclinic anisotropy. For this fibrous anisotropy, a fourth‐order elastic tensor is derived to define the constitutive relations between stress tensor and strain tensor. Components of this elastic tensor involve two Lame's moduli, eight fibroelastic coefficients and the angular deviation between two obliquely inclined fibre‐families. The velocities of bulk waves are calculated for propagation along general direction in this anisotropic composite. Propagation of surface wave is considered along the stress‐free plane boundary of anisotropic elastic half‐space. In a coordinate system with coordinate planes deviating from the plane boundary of the medium and/or plane of anisotropic symmetry, the fibrous composite is treated as triclinic for mathematical convenience. Mathematical model is derived to calculate the phase velocity of the surface wave, which varies with direction on the plane boundary. Horizontal energy flux at the boundary is calculated to determine the group velocity and ray direction of the surface wave. Effects of fibre‐orientations are analysed, numerically, on the wave velocities and ray direction of surface wave.

An Earth-fixed observer to ship waves

This work deals with the linear surface waves generated by a vessel advancing at a constant forward speed. These waves, known as ship waves, appear stationary to an observer on the vessel. Rather than exploring the well-studied stationary ship waves, this work delves into the physical properties of ship waves measured at Earth-fixed locations. While it might have been expected that analysing these waves in an Earth-fixed coordinate system would be a straightforward transformation from existing analytical theories in a moving coordinate system, the reality proves to be quite different. The properties of waves measured at fixed locations due to a passing ship turn out to be complex and non-trivial. They exhibit unique characteristics, being notably unsteady and short crested, despite appearing stationary to an observer on the generating vessel. The analytical expressions for the physical properties of these unsteady waves are made available in this work, including the amplitude, frequency, wavenumber, direction of propagation, phase velocity and group velocity. Based on these newly derived expressions and two-point measurements, an inverse method has been presented for determining the advancing speed and the course of motion of the moving ship responsible for the wave generation. The results from this study can be used in a wide range of applications, such as interpreting data from point measurements and assessing the roles of ship waves in transporting ocean particles.

Reverse time migration angle gathers in acoustic anisotropic media using direction vectors

The application of direction vectors in the generation of reverse time migration (RTM) angle gathers in complex acoustic anisotropic media often encounters three main challenges: not pointing to the phase-velocity direction (PVD) of the Poynting vector, inaccuracy due to overlapping wavefields, and instability due to zero points of the direction vector. In general anisotropic media, the standard Poynting vector indicates the group-velocity direction (GVD), whereas reflection and transmission phenomena rely on the PVD. Anisotropy introduces discrepancies between the GVD and the PVD. To overcome this issue, we use the so-called PVD vector to directly calculate the PVD from anisotropic wavefields, eliminating the need for an approximated conversion from the GVD to the PVD. To mitigate the inaccuracy problem, we apply the Hilbert transform-based wavefield decomposition method to separate overlapping wavefields into their up/down components, and then we calculate the PVDs using the separated wavefields. To tackle the instability problem, we incorporate the additionally simulated quadrature wavefield during the wavefield decomposition procedure. By combining the direction vector of the quadrature wavefield with that of the original wavefield, we can eliminate the zero points and thus obtain a stabilized PVD vector. With those problems solved or alleviated, we present a scheme for the generation of anisotropic RTM angle gathers in complex areas. Two numerical examples using synthetic data sets demonstrate our method’s effectiveness.

Acoustically driven spin wave resonance in Ni/128° Y-cut LiNbO3 hybrid devices with the beam steering effect

We study the acoustically driven spin wave resonance (ADSWR) in a Ni film sputtered on a 128° Y-cut lithium niobate (LiNbO3) substrate under the condition that the beam steering effect exists due to the surface acoustic waves (SAWs) transmitted along several selected crystal orientations. SAW devices with that effect exhibit significantly different ADSWR spectra from devices without it. By using the magnetoelastic coupling theory and finite element simulation associated with SAW, we find that the beam steering effect of magnetoacoustic waves has an important influence on the acoustic attenuation. The relationship between its group velocity direction and the magnetization vector can be used to define the magnetoacoustic wave mode. The mode affects acoustic attenuation magnitude, which can break the fourfold symmetry. Increasing its power flow angle will significantly increase the maximum acoustic attenuation caused by magnon–phonon coupling.

The Electromagnetic Ion Cyclotron Instability Affected by the Temperature Anisotropic Electrons in the Inner Magnetosphere

AbstractElectromagnetic ion cyclotron (EMIC) instabilities in the inner magnetosphere are investigated with considering the effect of temperature anisotropic electrons. The perpendicular anisotropic electrons (Ae > 1) impose an inhibiting effect on EMIC instabilities, whereas parallel anisotropic electrons (Ae < 1) may generate a promoting or inhibiting effect depending on the direction of wave group velocity. The electron firehose modes can be coupled with EMIC modes. Three unanticipated secondary waves nearby the ion cyclotron frequencies are aroused by the electrons resonating with EMIC waves. The strong wave growth at proton gyrofrequency indicates that the electrons as an important energy provider for EMIC modes have been largely overlooked in previous studies. For the first time, we report a backward EMIC wave with the group velocity in opposite direction of the phase velocity. We suggest the new‐found effects from hot anisotropic electrons may improve our understanding of EMIC instabilities in the inner magnetosphere.

Inertial wave attractors in librating cuboids

Perturbed rapidly rotating flows are dominated by inertial oscillations, with restricted group velocity directions, due to the restorative nature of the Coriolis force. In containers with some boundaries oblique to the rotation axis, the inertial oscillations may focus upon reflections, whereby their energy increases whilst their wavelength decreases and their trajectories focus onto attractor regions. In a linear inviscid setting, these attractors are Delta-like distributions. The linear inviscid setting is obtained formally by setting both Ekman number ${E}$ (ratio of inertial to viscous time scales) and Rossby number ${Ro}$ (non-dimensional amplitude of the forcing that drives the inertial oscillations) to zero. These settings raise fundamental questions, in particular concerning the nature of energy dissipation in the vanishing Ekman number regime. Here, we consider a simple container geometry, a rectangular cuboid, in which the direction of the rotation axis is oblique to four of its walls, subject to librational forcing (small-amplitude harmonic oscillations of the rotation rate). This geometry allows for accurate and efficient direct numerical simulations of the three-dimensional incompressible Navier–Stokes equations with no-slip boundary conditions using a spectral-Galerkin spatial discretisation along with a third-order temporal discretisation. Solutions with Ekman and Rossby numbers as small as ${E}={Ro}=10^{-8}$ reveal many details of how the inertial oscillations focus, at the libration frequency considered, onto attractors, and how the focusing leads to increased localised nonlinear and dissipative processes as ${E}$ and ${Ro}$ are reduced. Even for extremely small forcing amplitudes, nonlinear effects have important dynamic consequences for the attractors.

Acceleration strategy of source iteration method for the stationary phonon Boltzmann transport equation

Mesoscopic numerical simulation has become an important tool in thermal management and energy harvesting at the micro/nano scale, where the Fourier's law failed. However, it is not easy to efficiently solve the phonon Boltzmann transport equation (BTE) from ballistic to diffusive limit. In order to accelerate convergence, an implicit synthetic iterative scheme is developed for the stationary phonon BTE, in which a macroscopic moment equation is invoked and solved iteratively coupled with the typical source iteration of the kinetic equation. Different from previous numerical interpolation, the phonon BTE is solved again at the cell interface along the group velocity direction within a certain length when reconstructing the interfacial phonon distribution function. Fourier stability analysis shows that the present method could converge faster than the source iteration method in the (near) diffusive regime. Numerical results prove that the present scheme can capture the ballistic-diffusive effects correctly and efficiently. The present acceleration framework could be a powerful tool for simulating practical thermal engineering problems in the future.

Spin-velocity locking in a helical chain of atomic p± orbitals.

Observations of a high spin selectivity in various helical structures, which is called the chirality-induced spin selectivity, suggest a common mechanism originating from the helical geometry. In this paper, we consider a helical chain of atomic p± orbitals having the tangential angular momentum l = ±1. We show in this model that the coupling of l and the spin gives rise to spin-velocity locking, i.e., directions of spin and group velocity are parallel or antiparallel depending on the chirality of the helix, and consequently, an almost perfect spin selectivity in a specific energy region in a wide range of the curvature and the torsion of the helix. We find that the present spin-velocity locking originates from the helical symmetry in which the Hamiltonian is invariant with respect to a combined operation of the rotation around the helix axis and the translation along the helix axis. Therefore, we expect that spin-velocity locking occurs in a wide variety of helical structures.

Caustic spin wave beams in soft thin films: Properties and classification

In the context of wave propagation, caustics are usually defined as the envelope of a finite-extent wavefront; folds and cusps in a caustic result in enhanced wave amplitudes. Here, we tackle a related phenomenon, namely, the existence of well-defined beams originating solely from the geometric properties of the corresponding dispersion relation. This directional emission, termed caustic beam, is enabled by a stationary group velocity direction, and has been observed first in the case of phonons. We propose an overview of this ``focusing'' effect in the context of spin waves excited in soft, thin ferromagnetic films. Based on an analytical dispersion relation, we provide tools for a systematic survey of caustic spin wave beams. Our theoretical approach is validated by time-resolved microscopy experiments using the magneto-optical Kerr effect. Then, we identify two cases of particular interest both from fundamental and applicative perspectives. Indeed, both of them enable broadband excitations (in terms of wave vectors) to result in narrow-band beams of low divergence.

Low frequency band gap and vibration suppression mechanism of innovative multiphase metamaterials

In order to achieve low frequency vibration and noise reduction, researchers have found and explored many types of metamaterial structures. Based on this, an innovative multiphase metamaterial structure composed of hard materials and soft materials is proposed in this paper. According to Bloch’s theorem, the band gap characteristics of the proposed structure are calculated using the finite element method, and the formation mechanism of the band gap is analyzed. In addition, the effects of the stiffness and density of the two materials on the band gap are studied in detail. Then, the phase velocity, group velocity and wave propagation direction are calculated according to a certain frequency of the specific dispersion curve, and the important information of wave propagation in the structure is obtained. Finally, according to the transmission characteristics of vibration in a finite periodic structure, it is verified that the existence of band gap can inhibit the vibration transmission, and it is further clarified that the proposed structure has a good performance in the design of low-frequency band gaps with large amplitude.

Bandgap tuning and in-plane wave propagation of chiral and anti-chiral hybrid metamaterials with assembled six oscillators

In this paper, a hybrid acoustic metamaterial consisting of chiral and anti-chiral ligaments is proposed. The bandgap properties of the hybrid chiral and anti-chiral structure with and without oscillator intercalation are calculated using Bloch’s theorem and the finite element method, and the structure is verified and evaluated to have good vibration attenuation performance by means of transfer functions and stress clouds. By adjusting the resonant oscillator configuration and applying active strain, the structure is verified to have tunable capability, which provides a simple and easy scheme for bandgap tunability analysis. Finally, a comprehensive analysis of the structural vibration mode, phase constant plane, group velocity, phase velocity and wave propagation direction diagram lead to the conclusion that the directional and regional nature of wave propagation is responsible for the bandgap opening. The new structure in this paper provides a new way of thinking for vibration and noise reduction, and also provides a practical solution for bandgap adjustment. The comprehensive analysis of wave propagation also presents theoretical and technical support for the subsequent structure and bandgap optimization.

Low‐Frequency Vibration and Noise Reduction and Wave Propagation Properties of Hexagonal Hybrid Metamaterials with Local Resonance Strips

Based on the idea of local resonance, a class of hybrid acoustic metamaterials with interposed resonant strips is proposed in this article, and the bandgap characteristics and transmission properties are calculated by combining Bloch's theorem and lattice theory. The new structure is verified to have low‐frequency damping and noise reduction capability through the analysis of the stress cloud diagram at specific frequencies in the bandgap range. A comprehensive analysis of vibration modes, phase constant surfaces, group velocity, phase velocity, and wave propagation direction diagram is used to explore the wave propagation and bandgap opening mechanism, providing technical support and theoretical basis for subsequent bandgap optimization and structural improvement. The results show that this structure can open multiple bandgaps in the low‐frequency range below 500 Hz, and the stepped design of the single‐cell structure and the introduction of resonant strips provide a new design idea for low‐frequency vibration and noise reduction.

Determination of the phase-velocity direction in anisotropic media using a direction vector

Determination of the phase-velocity direction in anisotropic media is important in the general research of wave phenomena and in the construction of seismic modeling, imaging, and inversion algorithms for practical applications. By taking the dot-product of a scaled displacement vector with both sides of the elastic wave equation and rearranging terms, we identify two relevant computational formulas for the group-velocity and slowness vectors. The quantity in the numerator of this group-velocity vector is linked to the conventional Poynting vector which points in the group-velocity direction, and we thus refer to it as the direction vector for the group-velocity direction. Similarly, the quantity in the numerator of this slowness vector provides a new direction vector which points in the phase-velocity direction, and we thus refer to it as the direction vector for the phase-velocity direction. This new direction vector provides a convenient way to directly compute the phase-velocity direction by using extrapolated vector wavefields in general anisotropic media. We vali- date the effectiveness of the proposed Poynting vector for the phase-velocity direction by using an analytical relation in a homogeneous transversely isotropic medium. After that, three anisotropic models are used to show the differences between the group-velocity and phase-velocity directions, which are estimated by using the direction vectors for the group- velocity and phase-velocity directions. The proposed direction vector is also suitable for the computation of the phase-velocity direction in low-symmetry anisotropic media, including orthorhombic, monoclinic, or triclinic media.

Entrainment, stopping, and transmission of microwave solitons of self-induced transparency in counter-propagating magnetized electron beam.

Based on numerical simulations of a boundary problem, we study various scenarios of microwave soliton formation in the process of cyclotron resonance interaction of a short electromagnetic pulse with a counter-propagating initially rectilinear electron beam taking into account the relativistic dependence of the cyclotron frequency on the electrons' energy. When a certain threshold in the pulse energy is exceeded, the incident pulse can propagate without damping in the absorbing beam, similar to the effect of self-induced transparency in optics. However, mutual motion of the wave and electrons can lead to some novel effects. For relatively small energy of the incident pulse, the microwave soliton is entrained by the electron beam opposite to the direction of the wave's group velocity. With an increase in the pulse energy, soliton stopping occurs. This regime is characterized by the close-to-zero pulse velocity and can be interpreted as a variety of the "light stopping." High-energy microwave solitons propagate in the direction of the unperturbed group velocity. Their amplitude may exceed the amplitude of the incident pulse, i.e., nonlinear self-compression takes place. A further increase in the incident energy leads to the formation of additional high-order solitons whose behavior is similar to that of the first-order ones. The characteristics of each soliton (its amplitude and duration) correspond to analytical two-parametric soliton solutions that are to be found from consideration of the unbounded problem.

Advances in pseudo-magnetic field in artificial structures

<p indent=0mm>Pseudo-magnetic fields (PMFs) are firstly proposed in stretched graphene systems, in which the electrons behave as they do in a real magnetic field. Physically, the mechanical strain results in a lattice deformation and changes the hopping strength between carbon atoms, and thus induces an effective vector potential by shifting the Dirac points at the Brillouin zone. The PMF opens the door to control quantum transport by mechanical means and to explore unprecedented physics in a high-field regime, thus has drawn widespread attention recently. Inspired by the realization of strain-induced PMF in graphene, the concept of PMF is introduced into classical wave (e.g., optical and acoustic) systems using similar ways, because the strain tensor can also be written in the form of the vector potential within the tight binding approximation in classical wave systems. For classical wave systems that do not (or weakly) respond to external magnetic fields, the introduction of PMFs provides a new mechanism for controlling waves, and brings many physical properties analogous to those in real magnetic fields, such as Landau level quantization and quantum-Hall-like effect. Meanwhile, the macroscopic controllability enables the (optical or acoustic) artificial structure to provide an excellent macroscopic platform to explore PMFs and associated phenomena. In this review article, we introduce the recent progress of PMFs in artificial structures, especially on the construction routes of PMFs and related physical properties. The first classical PMF is realized in a triaxially deformed honeycomb photonic lattice, which consists of long dielectric waveguide arrays. Similarly, the PMF can be achieved in the other classical wave systems like microwave and acoustic systems by applying a triaxial strain field on the artificial structures or using the simulated strain effect by displacing the lattice sites. To simplify the experimental realization, a uniaxial strain field or deformation is proposed to realize the PMF in classical wave systems. Particularly, the microscopic controllability of artificial structures provides us a more simple approach to experimentally generate the PMF by engineering the individual unit-cell structure. By patterning the gradually varied unit-cell structures, the linearly varying vector potential can be realized in the gradient artificial structure, which results in a large uniform PMF. In such a system, the frequency-resolved spectrum is measured to demonstrate the Landau Levels induced by the PMF, and the quantum-Hall-like edge states are also observed. Benefiting from the macroscopic controllability of artificial structures, the PMF can be extended to 3D classical systems by engineering gradient artificial structures, in which the shifting of Weyl points effectively induces a gauge field. Particularly, in contrast to the zero-order Landau plateau in a 2D system with PMF, the zero-order chiral Landau level with linear dispersion is observed in 3D artificial structures with PMF. The zero-order chiral Landau level is characterized by one-way propagation, and the direction of group velocity is determined by the chirality of the Weyl point and the direction of PMF. The introduction of PMFs in 2D and 3D classical systems not only provides us a possibility to explore novel physics associated to the magnetic field without real magnetic field, but also opens the door to a wide range of potential applications, such as enhancing light or sound emission and nonlinear wave mixing due to the high density of states of Landau levels, optical or sound laser, and topological transports of the edge states under PMFs.

Instability of Supersonic Radiation Mode in Hypersonic Boundary Layers

The supersonic mode in hypersonic flows is studied numerically. The radiation characteristics of this mode in a flat-plate boundary layer with cooled walls are focused on. The linear stability analysis and a marching investigation using a parabolized stability equations approach are performed. Unlike the traditional bounded freestream boundary condition, a more physical boundary condition was proposed based on the group velocity direction of the supersonic mode. Two classes of the supersonic modes, the radiation mode and the incoming mode, are distinguished according to their different group velocities in wall-normal direction. The radiation mode is more unstable than the incoming one, for which it is the dominant instability. It is also found that both the stable and unstable radiation modes can radiate slow acoustic waves into the freestream, and no coalescence occurs between the radiation mode and the wave of the slow acoustic spectrum. This process can only be predicted by the linear stability theory with the new boundary condition. The slow acoustic wave has no effect on the supersonic radiation mode.

Spectral features of magnetic domain walls on the surface of three-dimensional topological insulators

We present a theoretical investigation of electron states hosted by magnetic domain walls on the 3D topological insulator surface. The consideration includes the domain walls with distinct vectorial and spatial textures. The study is carried out on the basis of the Hamiltonian for quasi-relativistic fermions by using a continual approach and tight-binding calculations. We derive the spectral characteristics and spatial localization of the the one-dimensional low-energy states appearing at the domain walls. The antiphase domain walls are shown to generate the topologically protected chiral states with linear dispersion, the group velocity and spin-polarization direction of which depend on an easy axis orientation. In the case of an easy plane anisotropy, we predict a realization of a dispersionless state, flat band in the energy spectrum, that is spin-polarized along the surface normal. Modification of the surface states in the multi-domain case, which is approximated by a periodic set of domain walls, is described as well. We find that the magnetic domain walls with complex internal texture, such as N\'eel-like or Bloch-like walls, also host the topological states, although their spectrum and spin structure can be changed compared with the sharp wall case.

Electromagnetic Wave Scattering from a Moving Medium with Stationary Interface across the Interluminal Regime

This paper extends current knowledge on electromagnetic wave scattering from bounded moving media in several regards. First, it complements the usual dispersion relation of moving media, ω(θk) (θk: phase velocity direction, associated with the wave vector, k), with the equally important impedance relation, η(θS) (θS: group velocity direction, associated with the Poynting vector, S). Second, it explains the interluminal-regime phenomenon of double-downstream wave transmission across a stationary interface between a regular medium and the moving medium, assuming motion perpendicular to the interface, and shows that the related waves are symmetric in terms of the energy refraction angle, while being asymmetric in terms of the phase refraction angle, with one of the waves subject to negative refraction, and shows that the wave impedances of the two transmitted waves are equal. Third, it generalizes the problem to the case where the medium moves obliquely with respect to the interface. Finally, it highlights the connection between this problem and a spacetime modulated medium.